During lunch hour at school, a group of five boys from Miss Jones' home room visited a nearby lunch wagon. One of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:

1. Rex: "Neither Earl nor I did it."

2. Jack: "It was Rex or Abe."

3. Abe: "Both Rex and Jack are liars."

4. Dan: "Abe's statement is not true; one of them is lying and the other is speaking the truth."

5. Earl: "What Dan said is wrong."

When Miss Jones was consulted, she said, "Three of these boys are knights, but two are liars." Assuming that Miss Jones is correct, can you determine who took the candy bar?

Since precisely three of these boys are knights, but two are liars, we examine each of the five cases wherein each of the five individuals in turn are guilty, and verify whetherthe respective number of liars and knights in each of thosefive situations conform to the given conditions.

These five situations are now examined in terms of the following table:

Situation Conclusion Remarks

Rex is Guilty Abe, Rex and Earl Contradiction are liars,and Jack and Dan are knights

Jack is Guilty Jack, Abe and Earl Contradiction are liars and Rex and Dan are knights

Dan is Guilty Jack, Abe and Dan Contradiction are liars,and Rex and Dan are knights

Earl is Guilty Rex, Jack and Dan Contradiction are liars,and Abe and Earl are knights

Abe is Guilty Abe and Dan are Conform to the liars,and Rex, Jack given conditions and Earl are knights